William is 3 times as old as Brandon. Eighteen years ago, William was 9 times as old as Brandon. How old is Brandon now?
Explanation: We can use the given information to write down two equations that describe the ages of William and Brandon. Let William's current age be $w$ and Brandon's current age be $b$ The information in the first sentence can be expressed in the following equation: $w = 3b$ Eighteen years ago, William was $w - 18$ years old, and Brandon was $b - 18$ years old. The information in the second sentence can be expressed in the following equation: $w - 18 = 9(b - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to use our first equation for $w$ and substitute it into our second equation. Our first equation is: $w = 3b$ . Substituting this into our second equation, we get: $3b$ $-$ $18 = 9(b - 18)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $3 b - 18 = 9 b - 162$ Solving for $b$ , we get: $6 b = 144.$ $b = 24$.